According to P.W. Joyce in English as we speak it in Ireland, first published in 1910, a caubeen is a shabby hat or cap from the Irish cáibín. This book wiill give the origin of most of the words you are looking for. I remember a line from an old song, "Put on your hat, my darling Pat and take off your old caubeen". I have always heard the term fardowns used for Northeners and another old song went " There never was a Corkie could lick a fardown"

Well, I'm pretty sure that I can figure this out – me being a self-proclaimed expert on this sort o' thing.

The "far" part of the word must come from the Irish word fear, which of course, means "man".
"Down" matches thíos which means "down", but also means "in the North".

heh, heh

Dúd - pipe hence the diminutive dúidín

Well here's another one that looks if it could come from Irish - Booligadhaun -

"You dundherheaded Booligadhaun!" says Father Cassidy, turning all the blame on Darby; "you mayandherin' Mayrauder of the Sivin Says!" he says. (that last part I can understand)

and - Tare an' ouns - does that mean anything to you?

aargh, you finally stumped me with Booligadhaun
It sure looks like it comes from the Irish language, but I can't quite make it out. This looks like a job for beagle or Bríd Mhór!

"Tare an' ouns" is the same as the exclamation "Tearin' 'ouns!" ("tearing wounds!")
By the way, there is another similar exclamation: "Blood an' 'ouns!" ("blood and wounds!")

Go raibh maith agat (agus oíche mhaith - or as we say here - bonne nuit )

Tá fáilte romhat.

Codhladh sámh … zzzzz …

Joyce has nothing on the booligadhaun or anything like it so it remains a mystery

From the context, and I'm only guessing here, Booligadhaun might come for the word "bog". Soft-headed. But I can't think of an actual word that is used that would be similiar to "bogadán".

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It is recommended that you always wait for three to agree on a translation.
I speak Connemara Irish, and my input will often reflect that.
I will do an mp3 file on request for short translations.
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And it could be something the author misheard. Since she didn't have Irish and almost certainly didn't speak Hiberno-English, the word is her interpretation of what she thought was said